A308768 Sum of the smallest parts of the partitions of n into 4 squarefree parts.

0, 0, 0, 0, 1, 1, 2, 2, 5, 5, 7, 8, 12, 11, 16, 16, 23, 23, 30, 32, 44, 43, 56, 57, 72, 72, 90, 87, 114, 112, 135, 137, 169, 164, 197, 196, 233, 238, 282, 276, 337, 332, 381, 378, 454, 447, 525, 523, 606, 609, 698, 678, 800, 799, 907, 895, 1050, 1022, 1157

Offset

0,7

Links

Table of n, a(n) for n=0..58.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k)^2 * k, where mu is the Möbius function (A008683).

a(n) = A308783(n) - A308762(n) - A308769(n) - A308770(n).

Mathematica

Table[Sum[Sum[Sum[k * MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Crossrefs

Cf. A008683, A308762, A308767, A308769, A308770, A308783.

Sequence in context: A168391 A157123 A265764 * A213032 A307984 A370585

Adjacent sequences: A308765 A308766 A308767 * A308769 A308770 A308771

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved